# Algebra ICCSS Regents Exam 0116Page 1

Algebra ICCSS Regents Exam 0116Page 1

1In the function , the minimum value occurs when x is

1) / / 3) /2) / 2 / 4) / 4

2The graph below was created by an employee at a gas station.

Which statement can be justified by using the graph?

1) / If 10 gallons of gas was purchased, $35 was paid. / 3) / For every 2 gallons of gas purchased, $5.00 was paid.2) / For every gallon of gas purchased, $3.75 was paid. / 4) / If zero gallons of gas were purchased, zero miles were driven.

3For a recently released movie, the function models the revenue earned, y, in millions of dollars each week, x, for several weeks after its release. Based on the equation, how much more money, in millions of dollars, was earned in revenue for week 3 than for week 5?

1) / 37.27 / 3) / 17.062) / 27.16 / 4) / 10.11

4Given the following expressions:

I. III.

II. IV.

Which expression(s) result in an irrational number?

1) / II, only / 3) / I, III, IV2) / III, only / 4) / II, III, IV

5Which inequality is represented by the graph below?

1) / / 3) /2) / / 4) /

6Michael borrows money from his uncle, who is charging him simple interest using the formula . To figure out what the interest rate, r, is, Michael rearranges the formula to find r. His new formula is r equals

1) / / 3) /2) / / 4) /

7Which equation is equivalent to ?

1) / / 3) /2) / / 4) /

8The equation is being used to calculate the amount of money in a savings account. What does 1.02 represent in this equation?

1) / 0.02% decay / 3) / 2% decay2) / 0.02% growth / 4) / 2% growth

9The zeros of the function are

1) / 3 and / 3) / and 12) / 3 and 1 / 4) / and

10When is subtracted from , the result is

1) / / 3) /2) / / 4) /

11Joe has a rectangular patio that measures 10 feet by 12 feet. He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x. Which equation could be used to determine x?

1) / / 3) /2) / / 4) /

12When factored completely, is

1) / / 3) /2) / / 4) /

13The table below shows the cost of mailing a postcard in different years. During which time interval did the cost increase at the greatest average rate?

Year / 1898 / 1971 / 1985 / 2006 / 2012Cost (¢) / 1 / 6 / 14 / 24 / 35

1) / 1898-1971 / 3) / 1985-2006

2) / 1971-1985 / 4) / 2006-2012

14When solving the equation by completing the square, which equation is a step in the process?

1) / / 3) /2) / / 4) /

15A construction company uses the function , where p is the number of people working on a project, to model the amount of money it spends to complete a project. A reasonable domain for this function would be

1) / positive integers / 3) / both positive and negative integers2) / positive real numbers / 4) / both positive and negative real numbers

16Which function is shown in the table below?

x / f(x)0 / 1

1 / 3

2 / 9

3 / 27

1) / / 3) /

2) / / 4) /

17Given the functions and , which value of x makes ?

1) / / 3) / 32) / 2 / 4) /

18Which recursively defined function represents the sequence ?

1) / / 3) /2) / / 4) /

19The range of the function defined as is

1) / / 3) /2) / / 4) /

20The graph of is shown below.

What is the graph of ?

1) / / 3) /2) / / 4) /

21Which pair of equations could not be used to solve the following equations for x and y?

1) / / 3) /2) / / 4) /

22The graph representing a function is shown below.

Which function has a minimum that is less than the one shown in the graph?

1) / / 3) /2) / / 4) /

23Grisham is considering the three situations below.

I.For the first 28 days, a sunflower grows at a rate of 3.5 cm per day.

II.The value of a car depreciates at a rate of 15% per year after it is purchased.

III.The amount of bacteria in a culture triples every two days during an experiment.

Which of the statements describes a situation with an equal difference over an equal interval?

1) / I, only / 3) / I and III2) / II, only / 4) / II and III

24After performing analyses on a set of data, Jackie examined the scatter plot of the residual values for each analysis. Which scatter plot indicates the best linear fit for the data?

1) / / 3) /2) / / 4) /

25The function, , is shown in the table below.

x / t(x)/ 10

/ 7.5

1 / 5

3 / 2.5

5 / 0

Determine whether is linear or exponential. Explain your answer.

26Marcel claims that the graph below represents a function.

State whether Marcel is correct. Justify your answer.

27Solve the equation for y:

28The graph below shows the variation in the average temperature of Earth's surface from 1950-2000, according to one source.

During which years did the temperature variation change the most per unit time? Explain how you determined your answer.

29The cost of belonging to a gym can be modeled by , where is the total cost for m months of membership. State the meaning of the slope and y-intercept of this function with respect to the costs associated with the gym membership.

30A statistics class surveyed some students during one lunch period to obtain opinions about television programming preferences. The results of the survey are summarized in the table below.

**Programming Preferences**

Comedy / Drama

Male / 70 / 35

Female / 48 / 42

Based on the sample, predict how many of the school's 351 males would prefer comedy. Justify your answer.

31Given that , solve for x in terms of a and b:

32Jacob and Jessica are studying the spread of dandelions. Jacob discovers that the growth over t weeks can be defined by the function . Jessica finds that the growth function over t weeks is . Calculate the number of dandelions that Jacob and Jessica will each have after 5 weeks. Based on the growth from both functions, explain the relationship between and .

33Let represent the height of an object above the ground after t seconds. Determine the number of seconds it takes to achieve its maximum height. Justify your answer. State the time interval, in seconds, during which the height of the object decreases. Explain your reasoning.

34Fred's teacher gave the class the quadratic function .

a) State two different methods Fred could use to solve the equation .

b) Using one of the methods stated in part a, solve for x, to the nearest tenth.

35Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue from coffee sales. Data from nine days this past fall are shown in the table below.

Day1 / Day

2 / Day

3 / Day

4 / Day

5 / Day

6 / Day

7 / Day

8 / Day

9

High

Temperature, t / 54 / 50 / 62 / 67 / 70 / 58 / 52 / 46 / 48

**Coffee Sales, f(t)**/ $2900 / $3080 / $2500 / $2380 / $2200 / $2700 / $3000 / $3620 / $3720

State the linear regression function, , that estimates the day's coffee sales with a high temperature of t. Round all values to the nearest integer. State the correlation coefficient, *r, of the data to the nearest hundredth. Does r* indicate a strong linear relationship between the variables? Explain your reasoning.

36A contractor has 48 meters of fencing that he is going to use as the perimeter of a rectangular garden. The length of one side of the garden is represented by x, and the area of the garden is 108 square meters. Determine, algebraically, the dimensions of the garden in meters.

37The Reel Good Cinema is conducting a mathematical study. In its theater, there are 200 seats. Adult tickets cost $12.50 and child tickets cost $6.25. The cinema's goal is to sell at least $1500 worth of tickets for the theater. Write a system of linear inequalities that can be used to find the possible combinations of adult tickets, x, and child tickets, y, that would satisfy the cinema's goal. Graph the solution to this system of inequalities on the set of axes below. Label the solution with an S. Marta claims that selling 30 adult tickets and 80 child tickets will result in meeting the cinema's goal. Explain whether she is correct or incorrect, based on the graph drawn.

Algebra ICCSS Regents Exam 0116

1ANS:2PTS:2REF:011601aiNAT:F.IF.C.8

TOP:Vertex Form of a Quadratic

2ANS:2PTS:2REF:011602aiNAT:A.CED.A.2

TOP:Graphing Linear Functions

3ANS:3

PTS:2REF:011603aiNAT:F.IF.A.2TOP:Evaluating Functions

4ANS:1PTS:2REF:011604aiNAT:N.RN.B.3

TOP:Operations with RadicalsKEY:classify

5ANS:2PTS:2REF:011605aiNAT:A.REI.D.12

TOP:Graphing Linear Inequalities

6ANS:3PTS:2REF:011606aiNAT:A.CED.A.4

TOP:Transforming Formulas

7ANS:4

PTS:2REF:011607aiNAT:A.REI.B.4TOP:Solving Quadratics

KEY:completing the square

8ANS:4PTS:2REF:011608aiNAT:F.LE.B.5

TOP:Modeling Exponential Functions

9ANS:1

PTS:2REF:011609aiNAT:A.SSE.B.3TOP:Solving Quadratics

10ANS:3

PTS:2REF:011610aiNAT:A.APR.A.1TOP:Operations with Polynomials

KEY:multiplication

11ANS:2PTS:2REF:011611aiNAT:A.CED.A.1

TOP:Geometric Applications of Quadratics

12ANS:3PTS:2REF:011612aiNAT:A.SSE.A.2

TOP:Factoring PolynomialsKEY:higher power AI

13ANS:4

(1) (2) (3) (4)

PTS:2REF:011613aiNAT:F.IF.B.6TOP:Rate of Change

KEY:AI

14ANS:2

PTS:2REF:011614aiNAT:A.REI.B.4TOP:Solving Quadratics

KEY:completing the square

15ANS:1PTS:2REF:011615aiNAT:F.IF.B.5

TOP:Domain and Range

16ANS:4PTS:2REF:011616aiNAT:F.LE.A.2

TOP:Families of Functions

17ANS:1

PTS:2REF:011617aiNAT:A.REI.D.11TOP:Other Systems

KEY:AI

18ANS:3PTS:2REF:011618aiNAT:F.LE.A.2

TOP:Sequences

19ANS:2PTS:2REF:011619aiNAT:F.IF.A.2

TOP:Domain and RangeKEY:real domain, exponential

20ANS:1PTS:2REF:011620aiNAT:F.BF.B.3

TOP:Transformations with FunctionsKEY:bimodalgraph

21ANS:4PTS:2REF:011621aiNAT:A.REI.C.5

TOP:Solving Linear Systems

22ANS:3PTS:2REF:011622aiNAT:F.IF.C.9

TOP:Comparing FunctionsKEY:AI

23ANS:1PTS:2REF:011623aiNAT:F.LE.A.1

TOP:Families of Functions

24ANS:3

For a residual plot, there should be no observable pattern and a similar distribution of residuals above and below the x-axis.

PTS:2REF:011624aiNAT:S.ID.B.6TOP:Residuals

25ANS:

Linear, because the function has a constant rate of change.

PTS:2REF:011625aiNAT:F.LE.A.1TOP:Families of Functions

26ANS:

No, because the relation does not pass the vertical line test.

PTS:2REF:011626aiNAT:F.IF.A.1TOP:Defining Functions

KEY:graphs

27ANS:

PTS:2REF:011627aiNAT:A.REI.B.4TOP:Solving Quadratics

KEY:factoring

28ANS:

During 1960-1965 the graph has the steepest slope.

PTS:2REF:011628aiNAT:F.IF.B.6TOP:Rate of Change

KEY:AI

29ANS:

The slope represents the amount paid each month and the y-intercept represents the initial cost of membership.

PTS:2REF:011629aiNAT:F.LE.B.5TOP:Modeling Linear Functions

30ANS:

PTS:2REF:011630aiNAT:S.ID.B.5TOP:Frequency Tables

KEY:two-way

31ANS:

PTS:2REF:011631aiNAT:A.REI.B.3TOP:Solving Linear Inequalities

32ANS:

PTS:2REF:011632aiNAT:A.SSE.B.3TOP:Modeling Exponential Functions

KEY:AI

33ANS:

. The height decreases after reaching its maximum at until it lands at

PTS:4REF:011633aiNAT:F.IF.B.4TOP:Graphing Quadratic Functions

KEY:context

34ANS:

Two of the following: quadratic formula, complete the square, factor by grouping or graphically.

PTS:4REF:011634aiNAT:A.REI.B.4TOP:Solving Quadratics

KEY:quadratic formula

35ANS:

This indicates a strong linear relationship because r is close to -1.

PTS:4REF:011635aiNAT:S.ID.B.6TOP:Regression

KEY:linear with correlation coefficient

36ANS:

PTS:4REF:011636aiNAT:A.CED.A.1TOP:Geometric Applications of Quadratics

37ANS:

Marta is incorrect because

PTS:6REF:011637aiNAT:A.REI.D.12TOP:Graphing Systems of Linear Inequalities

KEY:graph